You are running a local fair, and one of booths has a prize wheel with 12...

You are running a local fair, and one of booths has a prize wheel with 12 slots: 4 light bulbs, 4 gear shifts, and 4 dollar signs. You have been called over to arbitrate a dispute. A customer says that they have been watching the prize wheel spin for an hour, and after 60 spins, they have seen the gear shift come up 24 times (the gear shift means that instead of winning a prize, the customer has to donate work time to the fair). The customer is claiming that that wheel is loaded in favor of the gear shift, and is a cheap way to lure unsuspecting people into doing volunteer work for your fair. What a terrible accusation! How will you save the reputation of your fair? You decide to run a p-test.

• State your Null Hypothesis:

• State your Alternative Hypothesis:

• Given the following p-test, what is your p-value?

Are these results statistically significant? Do you accept or reject the null hypothesis? How can you defend the reputation of your fair?

Solutions

Expert Solution

Null Hypothesis H0: True proportion of occurrence of gear shift is 1/3 or 0.33.

Alternative Hypothesis Ha: True proportion of occurrence of gear shift is greater than 1/3 or 0.33.

Standard error of proportion SE = = 0.0607042

Sample proportion, = 24/60 = 0.4

Test statistic z = ( - p)/ SE = (0.4 - 0.33)/0.0607042 = 1.15

p-value = P(z > 1.15) = 0.1251

Since, p-value is greater than 0.05 significance level, we fail to reject null hypothesis H0 and conclude that these results are not statistically significant and there is no strong evidence that true proportion of occurrence of gear shift is greater than 1/3. Thus, we can defend the reputation of your fair by stating that there is no significant evidence from the data that the wheel is loaded in favor of the gear shift.

orchestra answered 1 year ago

Next > < Previous

Related Solutions

The local county fair this summer has a challenge with a winning prize of $250. You...

The local county fair this summer has a challenge with a winning prize of $250. You have to throw a spear at an underwater target that is sitting 1 meter below the water’s surface in a water trough. The challenge is arranged such that you have to stand on a platform that places your eyes 3 m above the bottom of the trough (and therefore 3 vertical meters above the target). From your location, you see the target 30° below...

Question 1: You will receive a prize if both a fair coin lands "heads" AND a...

Question 1: You will receive a prize if both a fair coin lands "heads" AND a fair die lands "6". After the coin is flipped and the die is rolled you ask if AT LEAST ONE of these events has occurred and you are told "yes." a) Use an event tree to help calculate the probability of winning the prize b) Formally calculate the probability of you winning the prize, whilst answering these questions in each step of your answer...

3. [12 marks] Suppose a busy grocery store has several sampling booths set up for the...

3. [12 marks] Suppose a busy grocery store has several sampling booths set up for the same product. After a customer samples the product, they are asked if they are less likely, just as likely, or more likely to buy a competitor’s product. The results are provided below. For the purposes of this exam, you may assume that each customer is independent. Less likely Just as likely More likely 50 45 55 You are the data analyst in charge of...

6. You won the big prize in the California lottery and you have to choose one...

6. You won the big prize in the California lottery and you have to choose one of the following two payment plans: Payment Plan 1: If you choose this payment plan, you will receive semiannual payments for a fixed period of time. The first payment of Rs. 150,000 will be paid on January 01, 2007 and it will grow by 2% every six months. You will receive the last payment on January 01, 2016 Payment Plan 2: If you choose...

at the local county fair, you watch as a blacksmith drops a 0.50kg iron horseshoe into...

at the local county fair, you watch as a blacksmith drops a 0.50kg iron horseshoe into a bucket containing 25kg of water. If the initial temperature of the horseshoe is 450C and the initial temp of water is 23C, what is the equilibrium temp of the system?

You have won a competition , and can choose any one of the following prize: a....

You have won a competition , and can choose any one of the following prize: a. 100,000 now b. 180,000 at the end of give of five years from c. 11,400 forever d. 19,000for each of the 10 years e . 6,500next year, and increaseing by 5% per year forever after If the interest rate is 12% what do you choose?

Question 1- Suppose that one of every ten cereal boxes has a prize, Out of a...

Question 1- Suppose that one of every ten cereal boxes has a prize, Out of a shipment of n = 400 cereal boxes, find the probability that there are somewhere between 40 and 46 boxes with prizes. (Hint:use the dishonest coin principle with p = 0.1 to solve for the mean and standard deviation. Remember the probability is a decimal number, round the answer to the nearest hundredth.) Question 2- A normal distribution has a mean of 30 cm and...

The local county fair has provided enjoyment for area residents for many years. In recent years,...

The local county fair has provided enjoyment for area residents for many years. In recent years, attendance at the nine-day fair has increased, and the fair officials recognize the need to improve the controls over cash receipts. They asked you as their internal auditor to observe the collection of admission fees at the main entrance to the fairgrounds, investigate how cash receipts are recorded, and recommend improvements that can be implemented next year. The facts you obtained from performing these...

You have 2 fair six-sided dice: one that is red and one that is blue. You...

You have 2 fair six-sided dice: one that is red and one that is blue. You conduct a random experiment by rolling the red die first and then rolling the blue die. Use this information and answer questions 2a to 2e. 2a) Determine whether following statements are outcome or event. You roll a red 1 and blue 3. You roll a red 2 and blue 5. The sum of two dice is greater than 9. 2b) How many outcomes are there...

12. You have negotiated to buy a local small business for $200,000 that you estimate will...

12. You have negotiated to buy a local small business for $200,000 that you estimate will provide you net income (or net cash flow) of approximately $65,000 per year (after all cash costs and expenses) for the “foreseeable future.” What is the “Present Value” of this company based on its expected cash flows, assuming no significant growth in income, and assuming your required rate of return (or discount rate) is 25.0%? 13. Using the scenario above, what would your monthly...

Subjects